Tom Haines and Cheteshwar Pujara scored double centuries to complete the remarkable escape act on the final day to share a stand of 351 in 119 overs.
Arthur said: "At times in this game I thought we bowled outstandingly well and I thought the first hour this morning with Conners and Lakmal was proper Test cricket , it was excellent stuff.
"In the first innings I thought we got it right and there were times in the second innings when I thought we bowled well for scant reward but you've got to take your hat off, I thought this boy Haines played incredibly well and we know Cheteshwar Pujara is a world-class player.
"I was impressed with our cricket over four days, we didn't get the result we wanted but we certainly put pressure on in all departments at certain times of the game."
Haines batted for just short of 11 hours for 243 while Pujara was unbeaten on 201 from 387 balls as Sussex closed on 515 for 3,180 ahead after following on 331 behind.
The pair looked certain to bat through the day but Haines chipped Nick Potts to midwicket shortly before the close.
Derbyshire’s hopes of seeing an Easter parade of wickets rested with the second new ball which was only 16 overs old and for the first hour, Haines and Pujara had to fight hard to survive.
Haines was reprieved on 194 when he edged a cut at Alex Thomson but Madsen at slip could not hold on.
He made the most of it by completing the first double century of his career.
Derbyshire kept rotating their bowlers but there was no sign of a breakthrough until Pujara on 130 drove a swirling catch to long on where Billy Godleman failed to cling on.
Haines was missed for a third time in the next over when he cut Leus du Plooy hard to slip but Madsen again failed to take a sharp chance.
Pujara completed his 150 from 326 balls and the 300 stand was posted in 108 overs.
Derbyshire’s chances of victory had long gone when Haines’s marathon innings finally ended but Pujara completed his double hundred on a day to remember for Sussex.